Tools: Helpful & Unhelpful

Not sure I made the best teaching move today, but I had to try it. We explored Dan Meyer's "Will it hit the hoop?" task(s).

Act 1: Roll "Take 1"

• Agree on the question, "Will he make the basketball shot?"
• Ask students to make a series of guesses for a total of six takes.

Act 2: Ask for information
I typically ask students to think of information they would find useful in answering the question. Today, I went somewhere else with Mathematical Practice 5. I asked students to make two lists:

• List 1: Math tools that would be UNhelpful.
• List 2: Math tools that would be helpful.

This is the fourth and final week of the summer academy. My students have been exploring many math tools. I'll list the activity/task with the prevailing tool(s):

• Class height: Measurement, mean, median, mode, range
• Number Tricks: inverse operations
• Bucky the Badger: Tables
• Barbie Zip Line: Pythagorean Theorem, wrong models
• Taco Cart: Pythagorean Theorem
• Barbie Bungee: Measuring, Data collecting, Tables, Line of best fit, slope-intercept, Desmos
• In-N-Out Burger: Slope-Intercept, Functions
• Styrofoam Cups: Functions, slope-intercept
• Stacking Cups: functions, slope-intercept, Desmos
• Basketball shots: guess and check, tables, linear systems, Desmos
• Datelines: functions, Desmos, linear inequalities
• Vroom Vroom: Measuring, Data collecting, Desmos, function of best bit, quadratic equations

As you can see, many of our tasks were dominated by slope-intercept and Desmos. I didn't find their lists surprising.

I love how some students thought Desmos would be helpful, while others thought it'd be unhelpful. Those that found it unhelpful, wished you could insert images into Desmos so they could use sliders to find the path of Dan's shots. Boy, were they happy when they discovered you could import images. My first class was split down the middle: half thought slope-intercept might be useful and half didn't. It took a few convincing students to explain why Vroom Vroom was an example where a linear function was unhelpful.

Overall, I'm pleased with this approach, but I wouldn't do it with every task. It might confuse students that there's only one way to solve a task and detract from the importance of MP 5. I thought this was a fitting opportunity for students to mainly see the difference between a linear function and quadratic function. Specifically, I wanted them to see the advantages of using sliders in Desmos with a quadratic function instead of a linear function. I think students need to shuffle through their tool belt often and pick the right tools for the right task. I think today it was necessary. Dan has written about this or breaking students' tools. Moving forward, it's a matter of using this strategy at relevant times and not overusing it. However, I might be wrong altogether. That's where it's your turn to chime in...

Tomorrow: Des-Man!

Tools,
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